@MISC{Walsh97proceedingsof, author = {Toby Walsh and Toby Walsh (editor}, title = {Proceedings of IJCAI-97 Workshop: Empirical AI}, year = {1997} }

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Abstract

this paper, we introduce a systematic approach for constructing such assumptions. We propose a method and a tool for this purpose. The main idea is to use mathematical proofs and analysis of their failure as a systematic means for forming assumptions. A mathematical proof that a PSM solves a given problem usually enforces the introduction of assumptions to close gaps in the line of reasoning of the proof. It can therefore be viewed as a search process for hidden assumptions. Gaps that can be found in a failed proof provide already first characterizations of these assumptions. An assumption that implies the required lemma necessary to close the gap is a possible candidate we are looking for. That is, formulating this lemma as an assumption is a first step in finding and/or constructing assumptions that are necessary to ensure that the competence of a PSM is strong enough to achieve the goals as they are defined by the task. Using an open goal of a proof directly as an assumption normally leads to very strong assumptions. That is, these assumptions are sufficient to guarantee the correctness of the proof, but they are often neither necessary for the proof nor realistic in the sense that application problems will fulfil them. Therefore, further work is necessary to find improved characterizations for these assumptions. This is achieved by a precise analysis of their role in the completed proof that is used to retrace unnecessary properties of them. We provide tool support for this process by adapting the Karlsruhe Interactive Verifier (KIV) [5] for our purpose. It is the interactive character of the underlying tactical theorem prover of KIV that makes it suitable for hunting hidden assumptions. Instead of returning with a failure KIV returns with open goals that could not ...